Chapter Number
Generating natural interactive motion in android
based on situation-dependent motion variety
Takashi Minato & Hiroshi Ishiguro

Asada Project, ERATO, Japan Science and Technology Agency
Japan

1. Introduction
In order to develop a robot that can work in normal everyday situations, it is necessary to
discover the principles relevant to establishing and maintaining social interaction between
humans and robots. Even if short-term human-robot interaction can be performed by
implementing simple behaviors in a robot, it remains difficult to realize long-term social
interaction. We have explored the principles underlying natural human-robot
communication by development of an android which closely resembles a human being,
which is called an android science approach (Ishiguro, 2005).
Nass et al. (Nass et al., 1994) demonstrated that the human-computer relationship isfundamentally social and that a person's social response toward computers is automatic insocial situations. It is inferred from their studies that person's interpersonal responses
subconsciously expressed toward a robot (in other words, perceptual social illusion (Jacob &Jeannerod, 2005)) underlie the natural communication between the person and the robot.
The condition to elicit interpersonal behavior must be related to a mechanism to support
natural communication. The android science approach explores the boundary conditions toelicit subconscious interpersonal behavior toward an android from humans by investigating
methods to make the android more humanlike.
Humanlike body motions are necessary to implement humanlike behavior in an android.
There have been several studies on the generation of humanlike motion, including studies
on a model to generate human motion trajectories based on a neurocomputational approach(Flash & Hogan, 1985; Uno et al., 1989; Kawato, 1992; Schaal & Sternad, 2001), a study on thecontrol of a manipulator based on a model of motion trajectories of a person's arm (Kashima& Isurugi, 1998), and studies on a computer graphics (CG) animated characters, which haveshown that noise in the motion makes the character's motion more humanlike (Perlin, 1995;
Bodenheimer et al., 1999). These studies successfully generated a humanlike motion.
However, a humanlike motion specific to communication situations has not been considered.
The present study considers the human-like nature of a person's motion during interaction
with other people.
A person generally does not produce exactly identical motion when he/she repeats abehavior with the same intention, as shown in Fig. 1(a). In contrast, a robot is able to repeat

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Fig. 1. An example of motion decomposition in a reaching movement.
exactly identical motion with a purpose. A person's motion is diverse in that the motion
varies according to noises, mental and physical states, the social situation, and so on, even if
the person's intention does not change. We endow an android with motion variety in orderto make the android behavior more humanlike. If a person consciously or subconsciously
attributes a cause of motion variety in an android motion to such things as the android's
mental states, physical states, and the social situations, the person has more humanlike
impression toward the android.
We further consider the variety of human motion. We divide a person's motion into thefollowing two components (an example is shown in Fig. 1(b)):(i)
A motion that satisfies his/her intention.
(ii)
A motion change that is not relevant to the intention (a variation of the physicalproperties of the motion (i) such as its trajectory and velocity).
The motion variety described in the above means a variety in the motion change. Motion
generation models involving a signal-dependent noise have been proposed in studies
related to the variety of the motion change (Todorov & Jordan, 2002; Miyamoto et al., 2004).
This noise-based variety cannot be controlled even if the subject consciously attempts tocontrol or suppress this variety. In contrast, motion variety caused by such things as mental
strain or hesitation can be consciously controlled. We assume that the motion variety in an
intentional motion influences the human-like nature of the android behavior, even if an
observed motion change caused by the variety is small.
The present chapter hypothesizes that the motion change that is not relevant to a subject's
intention and can be consciously controlled influences the humanlike impression towards
the subject. In particular, we focus on motion variety in an intentional motion caused by theChapter Title (Header position 1,5)

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Fig. 2. Gestures to be modelled. A subject reaches out and touches an object or a person.
social relationship between the subject and another person. The present chapter concretely
takes up the motion of a subject reaching out and touching another person. Even a simple
reaching motion of a humanoid robot has not been studied with respect to how the changeof its properties due to social situations affects the impression of an observer toward therobot. As an extreme case, the present chapter models the motion difference between twocases in which a subject touches another person or an inanimate object through observing
the subject's behavior. We then examine how the presence of the motion variety in an
android motion influences the impression toward the android. In a psychologicalexperiment, as a third party, participants watch an android touches a person or an object
and report their impressions.

2. A model of human motion variety based on differences in social situation
The present chapter hypothesizes that motion variety in an intentional motion independentof uncontrollable noise contributes to the human-like nature of the motion. In order toexamine this hypothesis, we model the motion difference caused by the social relationshipbetween two persons in the motion of one reaching out and touching the other. It is,however, difficult to control the social relationship between two persons in an experiment.
As the extreme case, we consider the difference between a person-object relationship (Fig. 2,top) and an interpersonal relationship (Fig. 2, bottom). The person-object relationship is notsocial, but this chapter considers it as the least social relationship. We then construct amodel of the difference in the subject's arm movements in these two cases.
In order to construct the model, we set up the situations shown in Fig. 2 and measured thesubject's arm movements with a motion capture system (MAC 3D System, Motion Analysis
Corporation). The task of the subject was to reach out with the right hand and touch a box ora female experimenter in front of the subject. The hand position of the subject was measured
by attaching a marker to the back of the hand. The sampling rate was 60 Hz. The subject
touched the left shoulder, nose, and forehead of the experimenter and two spots on the box,
the heights of which are the same as those of the shoulder and forehead (box low and boxhigh). The subjects were seven male students. Some of the subjects were familiar with thefemale experimenter and others were not. All subject touched the target in the order of box
low, box high, left shoulder, nose, and forehead, once for each target (total of thirty-fivetrials). The subjects were told to touch the target and return their hand to the initial position.

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Fig. 3. An example of a subject's hand velocity (subject 1).
The analysis is not for the purpose of finding differences in motion common to all subjects
because the motion variation is caused by individuality in some cases. It is sufficient to finda feature to differentiate a subject-person relationship (interpersonal case) from a subjectobject relationship (impersonal case) within a subject. However, if the feature is not common
among the subjects, it may be difficult to obtain a common impression towards an android
in the later experiment. Therefore, we attempt to find a feature that is shared by the majorityof the subjects.
First, we calculated the absolute value of the hand velocity in order to facilitate the analysis.
The trajectory of the hand position was smoothed by a low-pass filter, and the velocity wascalculated by forward differences. We investigated the difference in the velocity profiles. As
an example, the results for a typical subject are shown in Fig. 3. Each plot is the absolutevalue of the velocity of the hand and is shifted in time so that the times of the first peaks are
the same. In each plot, the first bell-shaped curve indicates the reaching out motion, and thesecond bell-shaped curve indicates the returning motion. The following features were foundfor each subject.
z
The velocity profile in the reaching phase forms a unimodal, bell-shaped curve that
does not depend on the relationships (interpersonal and impersonal cases).
z
The velocity profile in the returning phase varies depending on the relationships.
There were no remarkable differences in motion among the subjects that were familiar withthe experimenter and the subjects that were not familiar with the experimenter. In order toexamine the returning phase in detail, the horizontal and vertical components of the velocity
were calculated. Figures 4 and 5 show the absolute value of the horizontal and verticalcomponents, respectively. In all cases, the profile of the vertical component in the returning

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Fig. 4. Horizontal velocity of the hand (the horizontal component of the Fig. 3).

Fig. 5. Vertical velocity of the hand (the vertical component of the Fig. 3).

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Fig. 6. An example of a subject's hand velocity (subject 2).

Fig. 7. An example of a subject's hand velocity (subject 3).
phase is a single-peak shape. This characteristic is common among all subjects. Moreover,the profile of the horizontal component in the returning phase has a peak before themaximum peak. Other examples of the horizontal and vertical components are shown in
Figs. 6 and 7. We can also find a similar profile of the horizontal component in theseexamples.
This characteristic appears 6 times among the 14 trials of the impersonal case and 18 times
among the 21 trials of the interpersonal case. In other words, this characteristic appears
more often in the interpersonal case than in the impersonal case. Although there is no
statistically significant difference between the two cases because the number of the subjects
is not sufficient, we focus on this feature in order to differentiate the interpersonal andimpersonal cases. Comparing the horizontal and vertical components, the time to start
increasing the vertical velocity is always later than the time to start increasing the horizontal
velocity. There is a tendency for this time delay to be larger in interpersonal cases than inimpersonal cases. These results suggest that, in the interpersonal case, when the subjects
returned their hands, they moved their hands horizontally at first and then brought theirhands down, whereas, in the impersonal case, subjects brought their hands down from theChapter Title (Header position 1,5)

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Fig. 8. The model of variation in returning phase of touching motion.
beginning. It is generally thought that a person moves his/her arm by controlling his/her
hand position initially with feedback control and then moves his/her arm in a ballistic
trajectory. This difference in motion can be modelled as the difference of desired hand
position of feedback control in the space close to another person (Fig. 8). To put it more
concretely:z
In the impersonal case, the desired hand position is set such that the hand can be
returned in the fastest path (Fig. 8, top).
z
In the interpersonal case, the desired hand position is set such that the hand can movefrom the space in proximity to the other person along the fastest path (Fig. 8, bottom).
Although this model is specific to the motion for touching another person or a box, it can betaken as a model of human motion variety due to differences in social situation. In the next
section, we examine the influence of the model on the impression towards an android.

3. Experiments
3.1 Repliee Q2 android
The android (called Repliee Q2) used in the experiment is shown in Fig. 9. The android ismodelled after a Japanese woman, the standing height of which is approximately 160 cm.

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Fig. 9. “Repliee Q2” android. The left figure is blurred in order to hide the details.

Fig. 10. Android motions generated based on the constructed model.
The skin is composed of a kind of silicone that feels like human skin. The android is driven
by pneumatic actuators that give it 42 degrees of freedom from the waist up. The legs andfeet are not powered. The android can neither stand up nor move from a chair. The joints
driven by the pneumatic actuator has mechanical flexibility in the control thanks to the highcompressibility of air. The flexibility of the joints makes for safer interaction, withmovements that are generally smoother than those of other similar systems. The
complicated dynamics of the air actuator make executing the trajectory tracking control
difficult.

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A motion with which theandroid touches an object
A motion with which theandroid touches a person

9Android A

Android B

Android C

Motion M1

Motion M2

Motion M1

Motion M1

Motion M2

Motion M2

Table 1. The experimental conditions.
3.2 Method
We implemented the motion variation based on the proposed model in the Repliee Q2android and investigated the impression toward the android from a third-person viewpointin psychological experiments. We showed video recordings of the android motions toparticipants and asked them impressions toward the android. The android motions
generated based on the proposed model are shown in Fig. 10. The top of the figure shows
the motion in which the hand is returned along the fastest path (hereafter, motion M1). The
bottom panel shows the motion in which the hand leaves from the space near the otherperson along the fastest path (hereafter, motion M2). The motion of reaching out was
implemented according to the average motion of the subjects' reaching motions observed in
the experiment described in Section 2. It is difficult to implement a quick and smooth
motion in the android with a simple feedback control because the joints are driven byflexible pneumatic actuators. In order to avoid this difficulty, we implemented the motionsin the android so that the speed of motion is slow. The video stimuli were made by playing
videos of the android with slow motion at fast speed.
In order to examine the influence of the motion variety on the impression toward theandroid, we prepared three types of android, as shown in Table 1. Three androids reach out
and touch persons and inanimate objects in different manners. The android in Condition A(hereafter, android A) touches persons and objects with motion M1. The android in
Condition B (hereafter, android B) touches persons and objects with motion M2. The
android in Condition C (hereafter, android C) touches objects with motion M1 and persons
with motion M2. Conditions A and B are used to examine the impressions with respect tothe androids without motion variety, and Condition C is used to examine the impressions
with respect to the androids with motion variety. When the target is a person, the android
touches the left shoulder of the person sitting in a face-to-face position.
In each condition, a participant was presented six android motions to report the impression.
The android touches three objects (a calendar, a video camera, and a small shelf) and threemale persons once for each target. The six targets are shown in Fig. 11. The video stimulus issynthesized from a video recording of the android motion without the target and a video
recording of the only target. The video of each motion is five seconds long. In each condition,
six motions were randomly presented to a participant with a constraint in which the motionof touching an object and the motion of touching a person were alternately presented. Inorder to eliminate memory effect and aftereffect, a blank image was presented for two
seconds between the videos, as shown in Fig. 12.
We designed a questionnaire using a five-point Likert scale with 1 = strongly disagree, 3 =neutral, and 5 = strongly agree. The aim of the questionnaire is to ask the impression of theandroid's human-like nature; therefore, the questionnaire asked how the android is“humanlike.” It is, however, possible that the variation in the arm trajectories does not
influence the impression on the human-likeness. We then prepared other six items in theName of the book (Header position 1,5)

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Fig. 11. The objects and persons in the video stimuli.

Fig. 12. The procedure to present the video stimuli.
questionnaire, which are likely influenced by the variation in the arm trajectories. The items
are ``the android is (1) polite, (2) accurate, (3) intellectual, (4) conscientious, (5) friendly, (6)graceful, and (7) humanlike.'' The items are listed in random order in order to avoid theorder effect, except for “humanlike,” which always appears at the end of the questionnaire,
because an answer to the item “humanlike” is likely to influence the responses to the otheritems.
3.3 Experiment 1: comparing Androids A and C
At first, we compared Androids A and C in order to investigate the influence of the presenceof motion variety in the android. The expectation is that the comparison of the impressionsof the human-like nature results in the following:
Android C > Android A.

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Fig. 13. The results of questionnaire about impressions towards Androids A and C.

Fig. 14. The results of questionnaire about impressions towards Androids A, B, and C.

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The participants were twenty-four university students (nineteen males and five females)
who were familiar with the Repliee Q2 android. Each participant participated in bothconditions, although the order of the conditions was changed randomly. The participant
answered the questionnaire after every condition was presented.
The average scores of the impressions are shown in Fig. 13. A paired t-test revealed
significant differences (p<0.05) in two conditions for the items of “polite” and “graceful,”although there was no significant difference for the item “humanlike.” The android
behavior in which the hand quickly moves from the space in proximity to the other person
likely gave an impression that the android carefully and deliberately touches the otherperson. It is inferred that the participants thought that the android had an intention oftouching the other person carefully. It is, therefore, that the participants thought that
Android C is politer and more graceful. It can be also said that the participants wereconsciously or subconsciously aware that Android C changed the hand trajectory from thefact that there are significant differences for some items.
Here, we consider the difference between Androids A and C. In Condition C, the android's
arm trajectory varies according to the android-target relationship, and in Condition A, theandroid's arm trajectory does not vary according to the android-target relationship. Another
difference is that, in Condition C, the android shows motion M2, which is not the case in
Condition A. In other words, there is a possibility that the presence of motion M2 produced
different impressions. In order to show that the different impressions are caused by thedifference in social situation, it is necessary to examine the influence of motion M2.
Therefore, in the next section, we conducted an additional experiment to assess the android
in Condition B.
3.4 Experiment 2: comparing Androids A, B, and C
The participants in this experiment were twelve of twenty-four participants who
participated in experiment 1. They were nine males and three females. Each participant waspresented Android B and answered the questionnaire about it. The expectation is that thecomparison of the impressions of the human-like nature results in the following:
Android C > Android A, Android B.
The average scores of the impressions toward Android B are shown in Fig. 14 by adding theresult to Fig. 13. Ryan's multiple comparison test revealed a significant difference (p<0.05)
between Androids A and C for the item “graceful.” This is the same result as the one
obtained in the experiment 1. Contrary to our expectation, however, there was no significant
difference between Androids B and C.
We then considered the influence of the order of stimulus presentation. The participants ofthe experiment 2 assessed in order of Androids A, C, and B or C, A, and B. Hereinafter, Case
O1 and Case O2 indicate the order of AÆCÆB and CÆAÆB, respectively. A repeatedmeasures two-way ANOVA with a factor of condition order and a factor of android motion
was conducted. There were significant interactions at the 5% level for the items of“intellectual”, “friendly”, and “humanlike” and at the 10% level for the item of“conscientious.” It is possible that the effect of the android motion on the impression score
depends on the order of conditions.

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We divided the twelve participants into participants who participated in Case O1 (sevenpersons) and participants who participated in Case O2 (five persons) and analyzed theirimpression scores. The average impression scores obtained in Cases O1 and O2 are shown in
Figs. 15 and 16, respectively. For each item, three conditions are rearranged in the order ofpresentation. Two tendencies can be seen in these figures:z
The scores obtained in the condition right after Condition C are smaller than those in
Condition C.
z
The scores obtained in the condition right after Condition A are larger than those in
Condition A.
Ryan's multiple comparison test revealed several significant differences at 5% level among
Androids A, B, and C as shown in Figs. 15 and 16. In particular, as expected, the score of“humanlike” for Android C is significantly larger than that for Android B in Case O1. In
Case O2, the participants thought the android which touched anything with the motion M2
was more deliberate and careful than the android which touched anything with the motion
M1. Furthermore, it is likely that this careful motion gave an impression that Android B was
more humanlike than Android A in Case O2. However, the participants thought that
Android C with motion variation was more humanlike than Android B when Android C
was presented just after Android B in Case O1. It is possible that the participants think theandroid with the motion variation is more humanlike than the android with only the carefulmotion.
3.5 Summary
The experimental results showed that the variety of the android motion enhances theimpression of human-like nature toward the android under the influence of the order ofstimulus presentation, although the expected result (i.e., Android C is more humanlike thanAndroids A and B) was not obtained. In addition, the results showed that motion variety
influences impressions such as “conscientious” and “graceful”, which are related to thehuman-like nature of the android. The number of participants of the experiments was too
few to compare the three conditions. The expected effect of the motion variety may beshown by an experiment with a larger number of participants.
As an example of motion variety, the present chapter examined the motion variation inwhich the desired hand position of feedback control varies in two ways when a person
returns his/her hand after touching a target. In addition, the social relationship whichcauses this variation was also designed to be varied in two cases, that is, android-person andandroid-object relationships. This is a simple example of variety. However, more
complicated motion variation can be designed, for example, by changing the causes of thevariation. It is inferred that complicated variation has a different influence on the impression,
although there are appropriate variations for enhancing the human-like nature. Further
investigation is necessary in order to clarify what motion variety makes the android
humanlike.
In Section 2, we assumed that the variation of the subject's arm motion is caused by thesocial relationship between the subject and the target. However, the subconscious motion
variation was not verified to be due to the social situation. There is another possibility, i.e.,that the variation is, for example, due to the hardness of the target, such as a hard box or asoft human body. In addition, it was not verified that the participants in Section 3 actually
attributed the cause of motion variation to the social situation, although the motion

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Fig. 15. Impressions of participants assessed in order of Androids A, C, and B (Case O1).

Fig. 16. Impressions of participants assessed in order of Androids C, A, and B (Case O2).

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variation conditionally enhanced the impression of the android's human-like nature. In
other words, it is not clear that the participants think Android C socially behaves likehuman beings. One possible design of an experiment is to compare with the android which
has same motions but different motion variation, that is, the android which touches objects
with motion M2 and persons with motion M1 (this manner is opposite to Android C). If thisandroid is less humanlike than Android C, the motion variation which is congruent withthat of human subjects shown in Section 2 contributes the human-likeness of the android.
However, further investigation is necessary to verify whether the social relationship caused
the arm motion variation observed in Section 2 and the different impressions toward theandroid obtained in Section 3.

4. Conclusion
We hypothesized that a motion variety that is not related to a subject's intention and can beconsciously controlled influences the humanlike impression of the subject, and we assumed
that this motion variety makes the android more humanlike. In order to verify thishypothesis, we constructed a model of the motion variety through the observation of
persons’ motions. We examined the variation in a motion of reaching out and touchinganother person, which occurred in different social relationships between the subject and theother person (or object). The experimental results showed that the modelled motion variety
conditionally influences the impression toward the android.
The results of the present chapter are specific to the android's motion of reaching out andtouching a person. The present study is a first step in the exploration of the principles forproviding natural robot behaviors. The results revealed that a phenomenon whereby motion
variety influences the impression towards the actor can be seen at least in certain motions ofa very humanlike robot. Based on these results, it is possible to examine which aspects of therobot's appearance and motion are affected by this phenomenon. This exploration will help
to clarify the principles underlying natural human-robot communication.
From the viewpoint of the robot motion design, a motion variety model is also useful.
Several studies have proposed a method by which to implement humanlike motion in ahumanoid robot by copying human motion as measured by a motion capture system to therobot (Riley et al., 2000; Nakaoka et al., 2003; Matsui et al. 2005). In order to make a robot
motion more humanlike, it is necessary to implement a humanlike motion variation.
However, it is not necessary to copy all human motions. This humanlike motion variation
can be automatically generated from an original motion by the motion variety model.

5. Acknowledgements
The android robot Repliee Q2 was developed in collaboration with Kokoro Company, Ltd.

6. References
Bodenheimer, B.; Shleyfman, A. V. & Hodgins, J. K. (1999). The effects of noise on theperception of animated human running, Computer Animation and Simulation '99:
Proceedings of the Eurographics Workshop, pp. 53-63, ISBN: 978-3-211-83392-6, Milano,
Italy, Sep., 1999, Springer-Verlag.

16

Name of the book (Header position 1,5)

Flash, T. & Hogan, N. (1985). The coordination of arm movements: An experimentallyconfirmed mathematical model, Journal of Neuroscience, Vol. 5, No. 7, pp. 1688-1703,
1985, ISSN: 0270-6474.
Ishiguro, H. (2005). Android science -toward a new cross-interdisciplinary framework,
Proceedings of the 12th International Symposium of Robotics Research, San Francisco,USA, Oct., 2005.
Jacob, P. & Jeannerod, M. (2005). The motor theory of social cognition: a critique. Trends in
Cognitive Sciences, Vol. 9, No. 1, pp. 21-25, 2005, ISSN: 1364-6613.
Kashima, T. & Isurugi, Y. (1998). Trajectory formation based on physiological characteristics
of skeletal muscles, Biological Cybernetics, Vol. 78, No. 6, pp. 413-422, 1998, ISSN :0340-1200.
Kawato, M. (1992). Optimization and learning in neural networks for formation and control
of coordinated movement, Attention and performance XIV, pp. 821-849, ISBN: 978-0262-13284-8, 1992, MIT Press.
Matsui, D.; Minato, T.; MacDorman, K. F. & Ishiguro, H. (2005). Generating natural motion
in an android by mapping human motion, Proceedings of the IEEE/RSJ International
Conference on Intelligent Robot Systems, pp. 1089-1096, ISBN: 0-7803-8912-3,
Edmonton, Alberta, Canada, Aug., 2005.
Miyamoto, H.; Nakano, E.; Wolpert, D. M. & Kawato, M. (2004). Tops (task optimization in
the presence of signal-dependent noise) model. Systems and Computers in Japan, Vol.
35, Issue 11, pp. 48-58, 2004, ISSN: 0882-1666.
Nakaoka, S.; Nakazawa, A.; Yokoi, K.; Hirukawa, H. & Ikeuchi, K. (2003). Generating wholebody motions for a biped humanoid robot from captured human dances,
Proceedings of the IEEE-RAS International Conference on Robotics and Automation, pp.
3905-3910, ISBN: 0-7803-7737-0, Taipei, Taiwan, Sep., 2003.
Nass, C.; Steuer, J. & Tauber, E. (1994). Computers are social actors, Proceedings of the ACM
Conference on Human Factors in Computing Systems, pp. 72-78, ISBN: 0-89791-651-4,
Boston, Massachusetts, USA, Apr., 1994.
Perlin, K. (1995). Real time responsive animation with personality, IEEE Transactions on
Visualization and Computer Graphics, Vol. 1, No. 1, pp. 5-15, 1995, ISSN: 1077-2626.
Riley, M.; Ude, A. & Atkeson, C. G. (2000). Methods for motion generation and interaction
with a humanoid robot: Case studies of dancing and catching, Proceedings of
AAAI/CMU Workshop on Interactive Robotics and Entertainment, pp. 35-42, Pittsburgh,
Pennsylvania, USA, Apr., 2000.
Schaal, S. & Sternad, D. (2001). Origins and violations of the 2/3 power law in rhythmic 3d
movements, Experimental Brain Research, Vol. 136, No. 1, pp. 60-72, 2001, ISSN: 00144819.
Todorov, E. & Jordan, M. I. (2002). Optimal feedback control as a theory of motor
coordination, Nature Neuroscience, Vol. 5, Issue 11, pp. 1226-1235, 2002, ISSN: 10976256.
Uno, Y.; Kawato, M. & Suzuki, R. (1989). Formation and control of optical trajectory inhuman multi-joint arm movement - minimim torque-change model, Biological
Cybernetics, Vol. 61, No. 2, pp. 89-101, 1989, ISSN: 0340-1200.